I've had this question for so long, I assume it stems from a basic misunderstanding about naturalism or metaphysics, so please set me straight.

Self-proclaimed naturalists (and/or materialists) have frequently made the claim to me that all that "exists" is a physical/material world, occasionally adding the correlate that physical bodies interact through forces/actions.

For my part, I've had trouble differentiating between forces (gravity, weak-strong forces, etc), motion, interaction -- which seem to be nonmaterial "things" which "exist" -- and the nonmaterial forces and substances of non-naturalists. I realize that "existence" for a force or action is probably a sloppy term, and that if pressed many naturalists would clarify that forces don't actually "exist" because they are not material. However, it seems to me the difference between naturalists and non-naturalists here is purely terminological -- naturalists simply define existence on the single criterion of being material while non-naturalists have a more flexible definition. In this case, the fact that all which exists is material is true for naturalists axiomatically.

Can anyone clarify this for me? Apologies if I have confounded a few technical definitions (feel free to set me straight on those as well).

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If you take the principle of inertia quite seriously, then by definition a force is a bookkeeping device (not unlike "potential energy") which accounts for the fact that objects occasionally accelerate. It proved to be useful to describe objects as accelerating to the extent that there is a net force on it, and also to suppose that forces can act on objects over distances, as with gravity. Newton didn't posit any particular reason why there should be such an influence without direct contact, and so it became somewhat natural to think of forces as non-local but real elements of the world, in a sense 'agents' to effect some influence from a body which was elsewhere. The importance of the notion of 'force' is exactly that: even if there isn't anything obvious which is causing an acceleration, we nevertheless assume that there is some external reason for the acceleration, and we only have to find out what. In this purest sense, 'force' could be parsed as "potentially unseen influence", where 'unseen' is meant to be interpreted literally, i.e. we may not have yet ascertained the reason.

In the time of Michael Faraday, especially in trying to understand magnetic forces, it proved useful to elaborate on the notion of force with the notion of a field. In this context, 'force' is just the word we use to describe the effect of a field on an object. In this reading, the 'force' is not exactly a thing unto itself, just as 'temperature' is not a thing unto itself, but rather a partial description of an interaction between things which do exist — fields and objects.

In modern physics, the fields which we considered previously are now understood to consist of gauge bosons (such as photons, gluons, etc.) which are transmitted between those particles which experience different forces — or in the case of gravity, space-time itself bends in response to the passage of matter, so that rather than fields in space interacting with matter we have space itself interacting with matter. Thus, for the moment, we seem to have closed much of the gap which was confusing in Newton's time; most forces are the effect of particles which are emitted and are absorbed or scattered, while gravity itself is reduced to geometry. "Fields" are used to describe collections of particles, including now matter particles which we have discovered have some things in common with those force-carrying fields which we imagined previously.

In each case, we have a theory of the world, and within that theory there are elements which we regard as "things which exist", and others which we regard as "features of the behaviour or interaction of the things which exist". Metaphysical naturalism — to the extent that it is not merely an ontological-flavoured proposition that the words 'real' and 'natural' are synonyms — can be regarded as an epistemological proposition, that nature is comprehensible in a systematic manner such as the three schema I've sketched out above: that is, for any collection of actual phenomena that you might care to consider, there is a model which encompasses all of those phenomena, in which we have a description of objects which interact. Were this true, it would follow that reality is governed by some set of "natural laws" (where the term 'law' denotes that there is structure in the behaviour of the universe), or at least can be represented as the limit point of some sequence of natural laws (with each 'law' in the sequence encompassing more phenomena than the last).

"Forces" are still around in our newer models of physics, but they are no longer regarded as things which 'exist', but rather a derived feature of the interaction of things that do. And indeed, many things which we now regard as "real" may turn out only to be effective descriptions of subtler phenomena. But these things which are "merely" effective descriptions of the world still reveal the world as a place of structure, and the point of naturalism is to reject that there are any aspects of reality which cannot be encompassed by any comprehensible structure.